Ch. 1: Econometrics of Event Studies 13
tests are well-specified only to the extent that the assumptions underlying their estima-
tion are correct. This poses a significant challenge because event study tests are joint
tests of whether abnormal returns are zero and of whether the assumed model of ex-
pected returns (i.e., the CAPM, market model, etc.) is correct. Moreover, an additional
set of assumptions concerning the statistical properties of the abnormal return measures
must also be correct. For example, a standardt-test for mean abnormal performance as-
sumes, among other things, that the mean abnormal performance for the cross-section
of securities is normally distributed. Depending on the specifict-test, there may be ad-
ditional assumptions that the abnormal return data are independent in time-series or
cross-section. The validity of these assumptions is often an empirical question. This is
particularly true for small samples, where one cannot rely on asymptotic results or the
central limit theorem.
3.5.2. Brown–Warner simulation
To directly address the issue of event study properties, the standard tool in event study
methodology research is simulation procedures that use actual security return data. The
motivation and specific research design is initially laid out inBrown and Warner (1980,
1985), and has been followed in almost all subsequent methodology research.
Much of what is known about general properties of event study tests comes from such
large-scale simulations. The basic idea behind the event study simulations is simple and
intuitive.^7 Different event study methods are simulated by repeated application of each
method to samples that have been constructed through a random (or stratified random)
selection of securities and random selection of an event date to each. If performance
is measured correctly, these samples should show no abnormal performance, on aver-
age. This makes it possible to study test statistic specification, that is, the probability
of rejecting the null hypothesis when it is known to be true. Further, various levels of
abnormal performance can be artificially introduced into the samples. This permits di-
rect study of the power of event study tests, that is, the ability to detect a given level of
abnormal performance.
3.5.3. Analytical methods
Simulation methods seem both natural and necessary to determine whether event study
test statistics are well-specified. Once it has been established using simulation methods
that a particular test statistic is well-specified, analytical procedures have also been used
to complement simulation procedures. Although deriving a power function analytically
for different levels of abnormal performance requires additional distributional assump-
tions, the evidence inBrown and Warner (1985, p. 13)is that analytical and simulation
methods yield similar power functions for a well-specified test statistic. As illustrated
below, these analytical procedures provide a quick and simple way to study power.
(^7) This characterization of simulation is fromBrown and Warner (1985, p. 4).